Robust tracking control for uncertain Euler-Lagrange systems via dynamic event-triggered and self-triggered ADP

This article investigates the robust tracking control problem for a class of Euler-Lagrange systems in presence of parameter uncertainties and external disturbances. Through system transformation and theoretical analysis, an adaptive dynamic programming (ADP) algorithm with two adaptive neural networks (NNs) and a suitable triggering mechanism is proposed to attain the robust stability of the closed-loop system. A single critic NN is leveraged to implement the approximate optimal controller design. Particularly, an NN-based feedforward compensation is developed to cope with the uncertainties with unknown bounds. Two different triggering mechanisms are respectively constructed to reduce the budget of sampling, communication and computation, namely the dynamic event-triggering mechanism (DETM) and the self-triggering mechanism (STM). The DETM is utilized to decide the update of remote controller and critic NN weight, which can yield a larger inter-event interval than the static event-triggering mechanism. Also, the Zeno-free behavior is guaranteed. Moreover, it is a novel attempt to introduce the STM into ADP design, which relaxes the demand of dedicated hardware online monitoring the event-triggering condition. Then it is demonstrated that all signals in the closed-loop system are uniformly ultimately bounded (UUB) via Lyapunov-based stability analysis. Finally, a simulation example of 2-link robotic system is implemented to verify the feasibility and effectiveness of the proposed algorithm.